Can you work out the dimensions of the three cubes?
This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the triangle.
A spider is sitting in the middle of one of the smallest walls in a
room and a fly is resting beside the window. What is the shortest
distance the spider would have to crawl to catch the fly?
"Efficient" could mean different things from different points of
view - maybe start by trying to minimise the amount of material
needed to make a tin with that volume.
What is the best diameter and height for a tin that contains $1$
litre of paint?